The Spanish side seemed set to qualify for the semifinals after Eliseu struck to put them 2-1 ahead on the night, and on aggregate, along with the away-goal edge.
Marco Reus drew Dortmund level in the first minute of injury time, though, before Felipe Santana scrambled home the winner from a seemingly offside position with just seconds to go, sparking wild celebrations among the hosts but furious protests from the visitors.
"They did not want us in the semifinals," an enraged Pellegrini said of the match officials. "After it went 2-1 for us, there were so many refereeing mistakes.
"The third goal was a hammer blow for us. There were two dismissals, and there was also their offside in the act of making it 3-2.
"In the final 10 minutes, we were so impaired (by the officials). In such conditions, everything becomes very difficult."
Pellegrini admitted that Malaga will struggle to get over the nature of its European exit, but called on his players to finish their Liga campaign on a high.
"It is certainly not a bitterness that will go away from one day to the next," Pellegrini said. "You can talk about a cruel defeat, but I do not agree, we have played a great game.
"Now we are looking to finish the championship as best we can."